Question 6 of 7: Cost-Volume-Profit Analysis — Bealing Company

Question 6: Cost-Volume-Profit Analysis — Bealing Company (8 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Sales $400,000; Variable costs $160,000; Contribution margin $240,000; Fixed costs $140,000; Operating profit $100,000.

Find. (a) The % increase in operating profit if sales rise 10% (via a smaller discount) with variable/fixed costs unchanged; (b) the change in operating profit if sales instead fall a further 2% (via a bigger discount), again with variable/fixed costs unchanged.

Approach. Because neither scenario changes unit volume or variable/fixed cost rates — only the net sales dollars collected, via the discount rate — every dollar of the sales change flows straight through to contribution margin and then to operating profit; there is no need to re-derive the contribution-margin ratio explicitly, though it is a useful cross-check.

1. Part (a) — 10% revenue increase. $$\text{New sales}=400{,}000\times1.10=\$440{,}000,\qquad \text{New CM}=440{,}000-160{,}000=\$280{,}000.$$ $$\text{New operating profit}=280{,}000-140{,}000=\boxed{\$140{,}000}.$$ $$\%\ \text{increase}=\frac{140{,}000-100{,}000}{100{,}000}=\boxed{40\%}.$$
2. Part (b) — additional 2% discount off the original sales. $$\text{New sales}=400{,}000\times(1-0.02)=\$392{,}000,\qquad \text{New CM}=392{,}000-160{,}000=\$232{,}000.$$ $$\text{New operating profit}=232{,}000-140{,}000=\boxed{\$92{,}000}.$$ $$\text{Change}=92{,}000-100{,}000=\boxed{-\$8{,}000\ \text{(a decrease)}}.$$